The computation MSE in (REF ) is a non-convex function of the AirComp filter \(\mathbf {g}\)  and the Tx-scaling factor \(\mathbf {b}\) .
To the best of the our knowledge,
there is no general approach to find the optimal \(\mathbf {g}\)  and \(\mathbf {b}\)  jointly. Therefore, we adopt the alternating minimization approach by alternately
solving problems (REF ) and (REF ) for \(\mathbf {g}\)  and \(\mathbf {b}\) , respectively, while fixing the other.
Note that alternating minimization is a widely applicable and empirically successful approach for optimization problems with different subsets of variables [1]}.
The effectiveness of the approach in the AirComp joint design problem will be verified via numerical results in the following section.
